Question

Problem 1: Symmetries of Newton's Laws In this problem, we will use the short-hand R(0) (sin θ cosθ (a) Two coordinate systems are related by a rotation: What is the relationship between the gradients V (,) and V(,,)? (b) Waves appear in a wide variety of physical systems and are described by the equation where V.VVs the Laplacian and c, is the speed of propagation. List al of the symmetries of this equation (c) Suppose we change the wave equation to the following which symmetries from part (b) are no longer symmetries whe|17 0. (d) when γ > 0, we would usually say that the wave is dixipating energy. Show this explicitly by finding the solutions to the equation for a fixed wavelength mode where k is a constant (the wavenumber) (e) Explain in words why the symmetry that was broken in (c) and energy dissipation are related. Hint: energy dissipation means energy is lost as we go to the future.

Answer 1

Soluton Given, Sin6 Coso since, J x thus ▽文 R(o) nner